Mathegoras

Coordinate geometry › Straight lines › Angle of inclination

Rotating a line to equal intercepts

High school · ●●●○○ 50 pts

The line y=10−2xy=10-2x is rotated anticlockwise about the origin through an angle θ\theta, where 0≤θ≤900 \le \theta \le 90 (in degrees). The image has xx-intercept (p,0)(p,0) and yy-intercept (0,q)(0,q). Determine θ\theta such that p=qp=q. Round to two decimal places.

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rotation matricesintercepts of a lineslope of a lineinverse trigonometric functions